The spatial covariant gravities represent a series of alternative modified theories of GR, which break time diffeomorphism invariance but preserve the spatial one [1]}, [2]}. This is very similar to the case of Hořava-Lifshitz (HL) theory of quantum gravity [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, in which the symmetry of the theory is broken from the general covariance down to the foliation-preserving diffeomorphisms. Such spatial covariance allows one to construct the action of the theory only in terms of spatial diffeomorphism invariants and study the effects of different terms. Those new terms, which are absent in the Einstein-Hilbert action of GR, provide an efficient way for parametrizing unknown high energy physics effects on the low energy scale. On the other hand, the spatial covariant gravities can also represent a very general framework for describing a lot of scalar-tensor theories at unitary gauge [1]}, [12]}. To our knowledge, a lot of scalar-tensor theories can be mapped to the spatial covariant framework by imposing the unitary gauge. To mention a few, these theories include: Horndeski theory, Chern-Simons modified gravity, Wely gravity, ghost-free parity violating gravities, \(D\rightarrow 4\)  Gauss-Bonnet gravity, Horava-Lifshitz gravities, etc, see details in ref. [13]}.
